restricting movements to x,y,z for the handicapped
You don't have to hold down they key, just press it once. So you should be able to do it with one hand.

The arrows/gizmo appears if you select the move/rotate/scale tool from the toolshelf (top left). That should allow you to control your objects using just the mouse.



You used to be able to draw gestures to control movement too, but I think that has gone now. This add-on looks like it might help in your case, but I haven't tried it myself: Gesture Ops